what can mathematics tell us about the treatment of cancer? in this talk i will present some of work that i have done in the modeling of tumor growth and treatment over the last ten years. cancer is a myriad of individual diseases, with the common feature that an individual's own cells have become malignant. thus, the treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells. mathematical models that describe tumor growth in tissue, the immune response, and the administration of different therapies can suggest treatment strategies that optimize treatment efficacy and minimize negative side-effects. however, the inherent complexity of the immune system and the spatial heterogeneity of human tissue gives rise to mathematical models that pose unique analytical and numerical challenges. in this talk i will briefly discuss two mathematical problems that we have encountered in our work: optimization of systems of delay differential equations, and the analysis of spatial models that incorporate different time scales. no knowledge of biology will be assumed.